that is observed. The conditional probabilities on these two situations are not necessarily or typically equal; they are related as follows:
P(physiological activity given deception) × P(deception)
=P(deception given physiological activity) × P(physiological activity).11
A strong ability to distinguish deception from truthfulness on the basis of a positive polygraph result requires that the polygraph test have high specificity (a probability of physiological response given nondeception close to zero). For example, a positive result from a test with 50 percent sensitivity and 100 percent specificity implies the subject is deceptive, but 50 percent of deceptive subjects will not be caught. A strong inference of innocence from a negative polygraph result requires that the sensitivity of the test be very high. In that case, all the deceptive subjects are caught, but unless the specificity is also high, many nondeceptive subjects will also be “caught.” Only with a test with an accuracy similar to that of DNA matching—which has both very high sensitivity and very high specificity—could one be confident that the test results correspond closely to truth.12 However, as we have shown, the physiological measures used in polygraph testing do not have such close correspondence with deception or any other single psychological state (Davis, 1961; Orne, Thackray, and Paskewitz, 1972). Lacking a one-to-one correspondence between the psychological and physiological states, empirical evidence at the aggregate level showing that deception produces larger physiological responses than honest responding does not adequately address the validity of the reverse inference, that larger physiological responses can be caused only by deception. This misinterpretation of the import of the empirical evidence has been called the “fallacy of the transposed conditional” in the literature on legal decision making (the attribution is usually to the statistician Dennis Lindley; see, e.g., Balding and Donnelley, 1995; Fienberg and Finkelstein, 1996). It is also known as the prosecutor’s fallacy because of the way it can arise in the courts. A prosecutor may offer forensic evidence that establishes the probability that a positive test result (a DNA match or a polygraph test indicating deception) would be observed if the defendant is innocent, but a jury’s task is to determine the probability that the defendant is innocent, given a positive test result.13 At least one jury decision has been overturned because of the confusion between these two probabilities (see Pringle, 1994).
Compounding the logical problems, many factors associated with polygraph testing itself may introduce substantial error, both random